Groups and Constraints: Symmetry Breaking during Search

@inproceedings{Gent2002GroupsAC,
  title={Groups and Constraints: Symmetry Breaking during Search},
  author={Ian P. Gent and Warwick Harvey and Tom Kelsey},
  booktitle={CP},
  year={2002}
}
We present an interface between the ECLiPSe constraint logic programming system and the GAP computational abstract algebra system. The interface provides a method for efficiently dealing with large numbers of symmetries of constraint satisfaction problems for minimal programming effort. We also report an implementation of SBDS using the GAP-ECLiPSe interface which is capable of handling many more symmetries than previous implementations and provides improved search performance for symmetric… 

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References

SHOWING 1-10 OF 17 REFERENCES

Symmetry Breaking in Constraint Programming

TLDR
This work describes a method for symmetry breaking during search (SBDS) in constraint programming that guarantees to return a unique solution from each set of symmetrically equivalent ones, which is the one found first by the variable and value ordering heuristics.

Symmetry-Breaking Predicates for Search Problems

TLDR
This work presents a general scheme whereby symmetries are exploited by adding \symmetry-breaking" predicates to the theory, and discusses methods for generating partial symmetry-breaking predicates, and shows that in several speciic cases asymmetries can be broken either fully or partially using a polynomial number of predicates.

Symmetry Breaking

TLDR
This work presents an approach that detects symmetric choice points during the search and enables the user to find solutions for complex problems with minimal effort spent on modeling.

Optimum Symmetry Breaking in CSPs Using Group Theory

TLDR
The research carried out has detailed how to exploit the symmetries in CSPs so that it will take less time to find unique solutions i.e. the authors will count two symmetrically equivalent solutions as one solution.

Excluding Symmetries in Constraint-Based Search

TLDR
This work introduces a new method, called symmetry excluding search (SES), for excluding symmetries in constraint based search, which is the first declarative method that can be applied to arbitrary asymmetries, and proves correctness, completeness and symmetry exclusion properties.

Symmetry in matrix models

TLDR
This work study and generalise symmetry-breaking techniques, such as lexicographic ordering, and proposes a labelling technique achieving the same effect.

Backtrack Searching in the Presence of Symmetry

TLDR
This paper gives the first algorithm that combines search rearrangement with an arbitrary symmetry group, and it is confirmed that the algorithms save a considerable amount of time on symmetric search problems.

Global Cut Framework for Removing Symmetries

TLDR
A general technique for removing symmetries in CSPs during search to record no-goods, during the exploration of the search tree, whose symmetric counterpart should be removed, and presents a general, correct and complete filtering algorithm for SRCs.

Symmetry Breaking in the Alien Tiles Puzzle

TLDR
This is the first integration of an algebraic system like GAP and a constraint programming system like ILOG Solver, based on the Alien Tiles game, and a 40-fold run-time provement over code with no symmetry breaking is obtained.

On the Reformulation of Vehicle Routing Problems and Scheduling Problems

TLDR
This paper presents a pre-processing transformation that "compresses" the VRP, transforming an element of travel into the duration of the visits, and reformulated as scheduling problem, to determine if it is primarily distance in theVRP that causes scheduling technology to degrade on the reformulated problem.